What is the integral from 0 to infinity of e^{-st} ?

The integral from 0 to infinity of e^{-st} is 1/s

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integral from 0 to infinity of e^{-st}

\int_{0}^{\infty} e^{- s t} d t

\frac{1}{s}

Solution steps

\int_{0}^{\infty} e^{- s t} d t

Compute the indefinite integral:

\int e^{- s t} d t = - \frac{1}{s} e^{- s t} + C

Compute the boundaries:

\int_{0}^{\infty} e^{- s t} d t = 0 - (- \frac{1}{s})

= 0 - (- \frac{1}{s})

Simplify

= \frac{1}{s}

y = (\frac{( 3 x ^{2} )}{2 x + 4})^{3}

x d y - y d x = (x y)^{\frac{1}{2}} d x

f (x) = 7 cos (x), at (\frac{2 π}{3})

x \to 1 lim (\frac{2 - x}{x - 1})

\frac{d}{d x} (x \cdot 2)

What is the integral from 0 to infinity of e^{-st} ?
The integral from 0 to infinity of e^{-st} is 1/s